Is 1680 is a composite number or not ?
- As we already know that, the number having factors 1 and the number itself is the prime number.
- And numbers having more than these two factors are the composite numbers.
- To check whether the number 1680 is composite or not first we have to find its factors.
Factors of 1680:
- If we have taken numbers from 1, 2, 3…for checking factors of 1680, we found that 1680 has factors 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840 and 1680. Hence, we must say that 1680 is a composite number.
- Thus, 1680 is the composite number.
- If we multiply 1680 by 1, 2, 3 then we get the multiples of 1680 which are 1680, 3360 and so on.
About the number 1680:
- 1680 has more than two factors which are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840 and 1680 and hence it is the composite number.
- 1680 is the even composite number and it is not the perfect square also.
- If we divide 1680 by 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840 and 1680 then we get remainder as zero. Hence, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840 and 1680 are the factors of 1680.
Note:
- 1680 is not the perfect square.
- Factors of 1680: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840 and 1680
- Prime factors of 1680: 2, 3, 5, 7
Conclusion:
- 1680 is the composite number which has factors 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840 and 1680
- And hence, 1680 is not the prime number.
Multiple Choice Questions:
1) 1680 is a
a) Even number
b) Odd number
c) Composite number
d) Both a and c
Ans: d) both a and c
2) The prime factors of a composite number 1680 are
a) 1680
b) 2, 3, 5, 7
c) 1, 4, 6, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840 and 1680
d) 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840 and 1680
Ans: b) 2, 3, 5, 7
3) 1680 is even composite number because
a) It has factors 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840 and 1680
b) It has more than two factors
c) Divisible by 2
d) all
Ans: d) all